# What do Abelian categories form?

@article{Kaledin2022WhatDA, title={What do Abelian categories form?}, author={Dmitry Kaledin}, journal={Russian Mathematical Surveys}, year={2022}, volume={77}, pages={1 - 45} }

Given two finitely presentable Abelian categories and , we outline a construction of an Abelian category of functors from to , which has nice 2-categorical properties and provides an explicit model for a stable category of stable functors between the derived categories of and . The construction is absolute, so it makes it possible to recover not only Hochschild cohomology but also Mac Lane cohomology. Bibliography: 29 titles.

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